It is not clear whether that number includes the more highly specialized teams, which by some estimates number only in the dozens and were described last month by Army Gen. David H. Petraeus, head of U.S. Central Command, as a handful of troops compared with the overall U.S. and allied force, which is increasing to more than 140,000.
McChrystal, a former head of JSOC, has supported the secret buildup, even while imposing restrictions on the use of air power as well as new rules on night raids. He was not given direct control of the teams, but as their former commander, he retains a large amount of influence over them.
Pentagon officials recently have realigned the command structure to give McChrystal control of the U.S. Marines and special operations forces that are mainly involved in training.
The Defense official said that with the new buildup, there will be more of the special operations forces in Afghanistan than there were in Iraq at the height of the U.S. troop buildup there in 2007.
"Although we will have less general purpose forces than we had in Iraq, we will have more special forces," the official said.
Within the military, some consider the work of the Joint Special Operations Command units in Iraq to have been key to calming the violence at the time.
Some of the additional JSOC teams sent to Afghanistan have been shifted from Iraq, where they worked to root out extremist cells aligned with Al Qaeda. Despite the recent flare-up in violence, officials say the number of extremists being sought in the Mideast nation has declined precipitously. Describing the change in the idiom of the secret units, a senior official said: "Hunting season is over in Iraq."
In Afghanistan, the special units have been following a playbook similar to the one they used in Iraq, and Defense officials hope the elite teams will have a similar effect on the overall level of security.
Defense officials emphasize that even the teams not under McChrystal's direct control are bound by his tactical directives.
"Rules are rules for everybody," said the Defense official.
"McChrystal holds them to a higher standard than conventional forces. When things go wrong, he is extremely aware of what the costs are."